A) \[2ax+2by-({{a}^{2}}+{{b}^{2}}+{{p}^{2}})=0\]
B) \[2ax+2by-({{a}^{2}}-{{b}^{2}}+{{p}^{2}})=0\]
C) \[{{x}^{2}}+{{y}^{2}}-3ax-4by+({{a}^{2}}+{{b}^{2}}-{{p}^{2}})=0\]
D) \[{{x}^{2}}+{{y}^{2}}-2ax-3by+({{a}^{2}}-{{b}^{2}}-{{p}^{2}})=0\]
Correct Answer: A
Solution :
Let equation of circle be \[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] with \[{{x}^{2}}+{{y}^{2}}={{p}^{2}}\] cutting orthogonally, we get \[0+0=+c-{{p}^{2}}\]or \[c={{p}^{2}}\] and passes through (a, b), we get \[{{a}^{2}}+{{b}^{2}}+2ga+2fb+{{p}^{2}}=0\] or \[2ax+2by-({{a}^{2}}+{{b}^{2}}+{{p}^{2}})=0\] Required locus as centre \[(-g,\ -f)\] is changed to (x, y).
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